Elena Baltacha powers on while Laura Robson earns test with Caroline Wozniacki

British No 1 Laura Robson on her way to a 6-3, 6-2 win over Yuliya Beygelzimer (Getty Images)

On a day when the defeat of Agnieszka Radwanska, the world No 5 and last year's Wimbledon runner-up, demonstrated the difficulties that grass-court tennis offers even to the very best, the current British No 1 and one of her predecessors proved the value of experience on the sport's most challenging surface.

Laura Robson and Elena Baltacha, who are into the second and third weeks respectively of their grass-court seasons, both won their opening matches in the Aegon International at Eastbourne. Robson beat a Ukrainian qualifier, Yuliya Beygelzimer, 6-3, 6-2, while Baltacha saw off the Czech Republic's Kristyna Pliskova 7-5, 7-6.

Radwanska, meanwhile, was playing her first match of the year on grass and was beaten 7-6, 6-2 by Jamie Hampton, of the United States. The 24-year-old Pole, who was the top seed, made a fight of the first set after an early break, but 23-year-old Hampton, who has reached two semi-finals this year and made the fourth round of the French Open, underlined her recent progress by dominating the second set.

Baltacha, who began her comeback in April after a lengthy absence during which she had ankle surgery, won the Aegon Challenge in Nottingham on Sunday – her first title for two years – and felt the benefit of the five matches she won last week as she beat an opponent ranked 82 places higher than her. Baltacha now faces Russia's Maria Kirilenko, the world No 10, who has won both their previous meetings.

"I'm playing well," Baltacha said. "Last week gave me a lot of confidence to know I can put my body through five days of matches. It was an amazing week for me."

Baltacha's ranking at No 185 in the world is a reflection more of the eight months she spent out of the game than her ability. The 29-year-old , who topped the national rankings just over a year ago, has returned with renewed ambition. One of her targets is the British No 1 spot currently held by Robson.

Anything other than a victory over Beygelzimer, the world No 187, would have been a surprise for Robson, but it was an important win for the world No 37 after her first-round defeat to Daniela Hantuchova, the eventual champion, at Edgbaston last week.

Next up is a much stiffer challenge against Caroline Wozniacki, a former world No 1 and the current No 9. Wozniacki, who was watched by her boyfriend Rory McIlroy after his return from the US Open golf tournament, has struggled of late, though she beat Robson in the first round of the French Open last month.

Johanna Konta failed to join her fellow Britons Robson, Baltacha and Heather Watson in the second round when she was beaten 6-4, 6-3 by the world No 44, Hsieh Su-wei, of Chinese Taipei. James Ward, the British No 2, went out of the men's event when he was beaten 6-3, 6-4 by Bernard Tomic.

Venus forced to miss Wimbledon

Five-time singles champion Venus Williams has pulled out of Wimbledon because of a back injury.

The 33-year-old struggled with the problem during the clay-court season and has not played since withdrawing from the doubles at Roland Garros with sister Serena.

Williams wrote on her Facebook page: "Unfortunately, I will not be able to participate in Wimbledon this year. I am extremely disappointed as I have always loved the Championships, but I need to take time to let my back heal."